We have discussed in the previous section implications for the extra Higgs bosons and predictions in the SM-like Higgs boson decays in the scenario where the axion has properties suggested by the XENON1T excess.
An interesting aspect of such axion from a cosmological point of view is that it can naturally explain the observed DM abundance, and it can also be probed by the future X-ray observatories, such as Theseus [1]}, [2]}, Athena [3]}, eROSITA [4]}, and XRISM [5]}.
While in the previous section the axion decay constant \(f_a\)  is fixed to reproduce the value of \(g_{ae}\)  suggestedb by the XENON1T excess, we here vary \(f_a\)  and investigate the connection between the axion coupling with electron \(g_{ae}\)  and the mass of additional Higgs bosons.
We then present the mass spectrum of the extra Higgs bosons if the axion is detected in the the future X-ray observatories.
In addition, one may be interested in the effect on the alignment parameters for the CP-even Higgs bosons \(\alpha _1\)  and \(\alpha _2\)  when considering testability of the axion.
To see how much these parameters can deviate from the alignment limit depending on the axion mass and the axion-electron coupling,
we numerically evaluate the possible size of deviations in the SM-like Higgs boson with the weak gauge bosons \(\kappa _V\) .
